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Home > Category Index for Science Quotations > Category Index P > Category: Proportion

Proportion Quotes (47 quotes)

À mesure que la science rabaisse ainsi notre orgueil, elle augmente notre puissance.
Science increases our power in proportion as it lowers our pride.
Original French quote from Introduction à l’étude de la médecine expérimentale (1865), 141. As translated in Fielding H. Garrison, 'Medical Proverbs, Aphorisms and Epigrams', Bulletin of New York Academy of Medicine (Oct 1928), 4, No. 10, 997. The translation above is literal. For a clearer interpretation, see another version on this web page: “But by a marvellous compensation, science, in humbling our pride, proportionately increases our power.”
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Ce grand ouvrage, toujours plus merveilleux à mesure qu’il est plus connu, nous donne une si grande idée de son ouvrier, que nous en sentons notre esprit accablé d’admiration et de respect.
[The Universe] This great work, always more amazing in proportion as it is better known, raises in us so grand an idea of its Maker, that we find our mind overwhelmed with feelings of wonder and adoration.
Original French and translation in Craufurd Tait Ramage (ed.) Beautiful Thoughts from French and Italian Authors (1866), 119-120.
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Mais, par une merveilleuse compensation, à mesure que la science rabaisse ainsi notre orgueil, elle augmente notre puissance.
But by a marvellous compensation, science, in humbling our pride, proportionately increases our power.
Original French quote from Introduction à l’étude de la médecine expérimentale (1865), 141. As translated by H.C. Greene in An Introduction to the Study of Experimental Medicine (1927, 1949), 82. Most often seen quoted in a shorter, more literal translation as “Science increases our power in proportion as it lowers our pride” (detailed elsewhere on this web page).
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A cosmic mystery of immense proportions, once seemingly on the verge of solution, has deepened and left astronomers and astrophysicists more baffled than ever. The crux ... is that the vast majority of the mass of the universe seems to be missing.
[Reporting a Nature article discrediting explanation of invisible mass being due to neutrinos]
In 'If Theory is Right, Most of Universe is Still “Missing”', New York Times (11 Sep 1984).
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And thus Nature will be very conformable to her self and very simple, performing all the great Motions of the heavenly Bodies by the Attraction of Gravity which intercedes those Bodies, and almost all the small ones of their Particles by some other attractive and repelling Powers which intercede the Particles. The Vis inertiae is a passive Principle by which Bodies persist in their Motion or Rest, receive Motion in proportion to the Force impressing it, and resist as much as they are resisted. By this Principle alone there never could have been any Motion in the World. Some other Principle was necessary for putting Bodies into Motion; and now they are in Motion, some other Principle is necessary for conserving the Motion.
From Opticks, (1704, 2nd ed. 1718), Book 3, Query 31, 372-3.
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Benford's Law of Controversy: Passion is inversely proportional to the amount of real information available.
In novel, Timescape (1992), no page numbering. The reference in the orginal text uses the past tense.
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De Morgan was explaining to an actuary what was the chance that a certain proportion of some group of people would at the end of a given time be alive; and quoted the actuarial formula, involving p [pi], which, in answer to a question, he explained stood for the ratio of the circumference of a circle to its diameter. His acquaintance, who had so far listened to the explanation with interest, interrupted him and exclaimed, 'My dear friend, that must be a delusion, what can a circle have to do with the number of people alive at a given time?'
Mathematical Recreations and Problems (1896), 180; See also De Morgan's Budget of Paradoxes (1872), 172.
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Every arsenate has its corresponding phosphate, composed according to the same proportions, combined with the same amount of water of crystallization, and endowed with the same physical properties: in fact, the two series of salts differ in no respect, except that the radical of the acid in one series in phosphorus, while in the other it is arsenic.
The experimental clue he used forming his law of isomerism. Originally published in 'Om Förhållandet emellan chemiska sammansättningen och krystallformen hos Arseniksyrade och Phosphorsyrade Salter', (On the Relation between the Chemical Composition and Crystal Form of Salts of Arsenic and Phosphoric Acids), Kungliga Svenska vetenskapsakademiens handlingar (1821), 4. Translation as shown in Joseph William Mellor, A Comprehensive Treatise on Inorganic and Theoretical Chemistry (1922), Vol. 1, 652. A very similar translation (“the same physical properties” is replaced with “nearly equal solubilities in water and acids”) is in F. Szabadváry article on 'Eilhard Mitscherlich' in Charles Coulston Gillispie (ed.), Dictionary of Scientific Biography (1974), Vol. 9, 424; perhaps from J.R. Partington, A History of Chemistry, Vol. 4 (1964), 210.
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I am particularly concerned to determine the probability of causes and results, as exhibited in events that occur in large numbers, and to investigate the laws according to which that probability approaches a limit in proportion to the repetition of events. That investigation deserves the attention of mathematicians because of the analysis required. It is primarily there that the approximation of formulas that are functions of large numbers has its most important applications. The investigation will benefit observers in identifying the mean to be chosen among the results of their observations and the probability of the errors still to be apprehended. Lastly, the investigation is one that deserves the attention of philosophers in showing how in the final analysis there is a regularity underlying the very things that seem to us to pertain entirely to chance, and in unveiling the hidden but constant causes on which that regularity depends. It is on the regularity of the main outcomes of events taken in large numbers that various institutions depend, such as annuities, tontines, and insurance policies. Questions about those subjects, as well as about inoculation with vaccine and decisions of electoral assemblies, present no further difficulty in the light of my theory. I limit myself here to resolving the most general of them, but the importance of these concerns in civil life, the moral considerations that complicate them, and the voluminous data that they presuppose require a separate work.
Philosophical Essay on Probabilities (1825), trans. Andrew I. Dale (1995), Introduction.
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I don’t know anything about mathematics; can’t even do proportion. But I can hire all the good mathematicians I need for fifteen dollars a week.
As quoted in French Strother, 'The Modern Profession of Inventing', World's Work and Play (Jul 1905), 6, No. 32, 187.
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I find in the domestic duck that the bones of the wing weigh less and the bones of the leg more, in proportion to the whole skeleton, than do the same bones in the wild duck; and this change may be safely attributed to the domestic duck flying much less, and walking more, than its wild parents.
From On the Origin of Species by Means of Natural Selection; or, The Preservation of Favoured Races in the Struggle for Life (1861), 17.
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I learned a lot of different things from different schools. MIT is a very good place…. It has developed for itself a spirit, so that every member of the whole place thinks that it’s the most wonderful place in the world—it’s the center, somehow, of scientific and technological development in the United States, if not the world … and while you don’t get a good sense of proportion there, you do get an excellent sense of being with it and in it, and having motivation and desire to keep on…
From Surely You’re Joking, Mr. Feynman!: Adventures of a Curious Character (1985), 51.
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I use the word “attraction” here in a general sense for any endeavor whatever of bodies to approach one another, whether that endeavor occurs as a result of the action of the bodies either drawn toward one other or acting on one another by means of spirits emitted or whether it arises from the action of aether or of air or of any medium whatsoever—whether corporeal or incorporeal—in any way impelling toward one another the bodies floating therein. I use the word “impulse” in the same general sense, considering in this treatise not the species of forces and their physical qualities but their quantities and mathematical proportions, as I have explained in the definitions.
The Principia: Mathematical Principles of Natural Philosophy (1687), 3rd edition (1726), trans. I. Bernard Cohen and Anne Whitman (1999), Book I, Section II, Scholium, 588.
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Imagination is more robust in proportion as reasoning power is weak.
In The New Science (3rd ed., 1744), Book 1, Para. 185, as translated by Thomas Goddard Bergin and Max Harold Fisch, The New Science of Giambattista Vico (1948), 63.
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In a large proportion of cases treated by physicians the disease is cured by nature, not by them. In a lesser, but not a small proportion, the disease is cured by nature in spite of them.
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In fact, Gentlemen, no geometry without arithmetic, no mechanics without geometry... you cannot count upon success, if your mind is not sufficiently exercised on the forms and demonstrations of geometry, on the theories and calculations of arithmetic ... In a word, the theory of proportions is for industrial teaching, what algebra is for the most elevated mathematical teaching.
... a l'ouverture du cours de mechanique industrielle á Metz (1827), 2-3, trans. Ivor Grattan-Guinness.
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In this generation, along with the dominating traits, the recessive ones also reappear, their individuality fully revealed, and they do so in the decisively expressed average proportion of 3:1, so that among each four plants of this generation three receive the dominating and one the recessive characteristic.
'Experiments on Plant Hybrids' (1865). In Curt Stern and Eva R. Sherwood (eds.), The Origin of Genetics: A Mendel Source Book (1966), 10.
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It is a scale of proportions which makes the bad difficult and the good easy.
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It is very remarkable that while the words Eternal, Eternity, Forever, are constantly in our mouths, and applied without hesitation, we yet experience considerable difficulty in contemplating any definite term which bears a very large proportion to the brief cycles of our petty chronicles. There are many minds that would not for an instant doubt the God of Nature to have existed from all Eternity, and would yet reject as preposterous the idea of going back a million of years in the History of His Works. Yet what is a million, or a million million, of solar revolutions to an Eternity?
Memoir on the Geology of Central France (1827), 165.
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Law 2: A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.
The Principia: Mathematical Principles of Natural Philosophy (1687), 3rd edition (1726), trans. I. Bernard Cohen and Anne Whitman (1999), Axioms, or Laws of Motion, Law 2, 416.
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Man has become a superman ... because he not only disposes of innate, physical forces, but because he is in command ... of latent forces in nature he can put them to his service. ... But the essential fact we must surely all feel in our hearts ... is that we are becoming inhuman in proportion as we become supermen.
Speech (4 Nov 1954) upon receiving the Nobel Peace Prize. In 'Excerpts From the Nobel Prize Address Dr. Schweitzer in Oslo', New York Times (5 Nov 1954), 4.
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Mathematics is a dangerous profession; an appreciable proportion of us go mad.
A Mathematician's Miscellany (1953). In Béla Bollobás, Littlewood's Miscellany (1986), 104.
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Men become civilized, not in proportion to their willingness to believe, but in proportion to their readiness to doubt.
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Nowadays everyone knows that the US is the world’s biggest polluter, and that with only one 20th of the world’s population it produces a quarter of its greenhouse gas emissions. But the US government, in an abdication of leadership of epic proportions, is refusing to take the problem seriously. … Emissions from the US are up 14% on those in 1990 and are projected to rise by a further 12% over the next decade.
In 'Global Warming is Now a Weapon of Mass Destruction', The Guardian (28 Jul 2003).
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Our delight in any particular study, art, or science rises and improves in proportion to the application which we bestow upon it. Thus, what was at first an exercise becomes at length an entertainment.
In The Spectator (2 Aug 1712), No. 447, collected in The Spectator (9th ed., 1728), Vol. 6, 225.
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Physiology is the basis of all medical improvement and in precise proportion as our survey of it becomes more accurate and extended, it is rendered more solid.
In 'An Inquiry, Analogical and Experimental, into the Different Electrical conditions of Arterial and Venous Blood', New Orleans Medical and Surgical Journal (1853-4), 10, 584-602 & 738-757. As cited in George B. Roth, 'Dr. John Gorrie—Inventor of Artificial Ice and Mechanical Refrigeration', The Scientific Monthly (May 1936) 42 No. 5, 464-469.
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Statistical accounts are to be referred to as a dictionary by men of riper years, and by young men as a grammar, to teach them the relations and proportions of different statistical subjects, and to imprint them on the mind at a time when the memory is capable of being impressed in a lasting and durable manner, thereby laying the foundation for accurate and valuable knowledge.
In The Statistical Breviary: Shewing, on a Principle Entirely New, the Resources of Every State and Kingdom in Europe (1801), 5-6.
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The amount of knowledge which we can justify from evidence directly available to us can never be large. The overwhelming proportion of our factual beliefs continue therefore to be held at second hand through trusting others, and in the great majority of cases our trust is placed in the authority of comparatively few people of widely acknowledged standing.
Personal Knowledge (1958), 208.
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The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to the effort it takes to see them.
In Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving (1981). As cited, with no more details, in Yi Ma, An Invitation to 3-D Vision (2004), 228.
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The extraordinary development of modern science may be her undoing. Specialism, now a necessity, has fragmented the specialities themselves in a way that makes the outlook hazardous. The workers lose all sense of proportion in a maze of minutiae.
'The Old Humanities and the New Science' (1919). In G. L. Keynes (ed.), Selected Writings of Sir William Osler (1951), 27.
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The faculty for remembering is not diminished in proportion to what one has learnt, just as little as the number of moulds in which you cast sand lessens its capacity for being cast in new moulds.
Religion: a Dialogue, and Other Essays (1890), 99.
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The faith of scientists in the power and truth of mathematics is so implicit that their work has gradually become less and less observation, and more and more calculation. The promiscuous collection and tabulation of data have given way to a process of assigning possible meanings, merely supposed real entities, to mathematical terms, working out the logical results, and then staging certain crucial experiments to check the hypothesis against the actual empirical results. But the facts which are accepted by virtue of these tests are not actually observed at all. With the advance of mathematical technique in physics, the tangible results of experiment have become less and less spectacular; on the other hand, their significance has grown in inverse proportion. The men in the laboratory have departed so far from the old forms of experimentation—typified by Galileo's weights and Franklin's kite—that they cannot be said to observe the actual objects of their curiosity at all; instead, they are watching index needles, revolving drums, and sensitive plates. No psychology of 'association' of sense-experiences can relate these data to the objects they signify, for in most cases the objects have never been experienced. Observation has become almost entirely indirect; and readings take the place of genuine witness.
Philosophy in a New Key; A Study in Inverse the Symbolism of Reason, Rite, and Art (1942), 19-20.
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The man who proportions the several parts of a mill, uses the same scientific principles [mechanics], as if he had the power of constructing an universe; but as he cannot give to matter that invisible agency, by which all the component parts of the immense machine of the universe have influence upon each other, and set in motional unison together without any apparent contact, and to which man has given the name of attraction, gravitation, and repulsion, he supplies the place of that agency by the humble imitation of teeth and cogs. All the parts of man’s microcosm must visibly touch.
In The Age of Reason: Being an Investigation of True and Fabulous Theology (27 Jan O.S. 1794), 42-43.
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The mathematics of cooperation of men and tools is interesting. Separated men trying their individual experiments contribute in proportion to their numbers and their work may be called mathematically additive. The effect of a single piece of apparatus given to one man is also additive only, but when a group of men are cooperating, as distinct from merely operating, their work raises with some higher power of the number than the first power. It approaches the square for two men and the cube for three. Two men cooperating with two different pieces of apparatus, say a special furnace and a pyrometer or a hydraulic press and new chemical substances, are more powerful than their arithmetical sum. These facts doubtless assist as assets of a research laboratory.
Quoted from a speech delivered at the fiftieth anniversary of granting of M.I.T's charter, in Guy Suits, 'Willis Rodney Whitney', National Academy of Sciences, Biographical Memoirs (1960), 352.
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The power of my [steam] engine rises in a geometrical proportion, while the consumption of fuel has only an arithmetical ratio; in such proportion that every time I added one fourth more to the consumption of fuel, the powers of the engine were doubled.
From 'On the Origin of Steam Boats and Steam Wagons', Thomas Cooper (ed.), The Emporium of Arts and Sciences (Feb 1814), 2, No. 2, 211-212.
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The primitive history of the species is all the more fully retained in its germ-history in proportion as the series of embryonic forms traversed is longer; and it is more accurately retained the less the mode of life of the recent forms differs from that of the earlier, and the less the peculiarities of the several embryonic states must be regarded as transferred from a later to an earlier period of life, or as acquired independently. (1864)
As translated and quoted in Ernst Haeckel and E. Ray Lankester (trans.) as epigraph for Chap. 13, The History of Creation (1886), Vol. 1, 406.
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The United States this week will commit its national pride, eight years of work and $24 billion of its fortune to showing the world it can still fulfill a dream. It will send three young men on a human adventure of mythological proportions with the whole of the civilized world invited to watch—for better or worse.
In 'Prestige of U.S. Rides on Apollo', Los Angeles Times (13 Jul 1969). As quoted and cited in Michael Collins, Carrying the Fire: An Astronaut’s Journey (2001), 315.
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There are … two fields for human thought and action—the actual and the possible, the realized and the real. In the actual, the tangible, the realized, the vast proportion of mankind abide. The great, region of the possible, whence all discovery, invention, creation proceed, and which is to the actual as a universe to a planet, is the chosen region of genius. As almost every thing which is now actual was once only possible, as our present facts and axioms were originally inventions or discoveries, it is, under God, to genius that we owe our present blessings. In the past, it created the present; in the present, it is creating the future.
In 'Genius', Wellman’s Miscellany (Dec 1871), 4, No. 6, 202.
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There is no area in our minds reserved for superstition, such as the Greeks had in their mythology; and superstition, under cover of an abstract vocabulary, has revenged itself by invading the entire realm of thought. Our science is like a store filled with the most subtle intellectual devices for solving the most complex problems, and yet we are almost incapable of applying the elementary principles of rational thought. In every sphere, we seem to have lost the very elements of intelligence: the ideas of limit, measure, degree, proportion, relation, comparison, contingency, interdependence, interrelation of means and ends. To keep to the social level, our political universe is peopled exclusively by myths and monsters; all it contains is absolutes and abstract entities. This is illustrated by all the words of our political and social vocabulary: nation, security, capitalism, communism, fascism, order, authority, property, democracy. We never use them in phrases such as: There is democracy to the extent that... or: There is capitalism in so far as... The use of expressions like “to the extent that” is beyond our intellectual capacity. Each of these words seems to represent for us an absolute reality, unaffected by conditions, or an absolute objective, independent of methods of action, or an absolute evil; and at the same time we make all these words mean, successively or simultaneously, anything whatsoever. Our lives are lived, in actual fact, among changing, varying realities, subject to the casual play of external necessities, and modifying themselves according to specific conditions within specific limits; and yet we act and strive and sacrifice ourselves and others by reference to fixed and isolated abstractions which cannot possibly be related either to one another or to any concrete facts. In this so-called age of technicians, the only battles we know how to fight are battles against windmills. [p.222]
…...
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There is no excellent beauty that hath not some strangeness in the proportions.
'Of Beauty.' Bacon's Essays (1880), Essay 43, 433.
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This king [Sesostris] divided the land among all Egyptians so as to give each one a quadrangle of equal size and to draw from each his revenues, by imposing a tax to be levied yearly. But everyone from whose part the river tore anything away, had to go to him to notify what had happened; he then sent overseers who had to measure out how much the land had become smaller, in order that the owner might pay on what was left, in proportion to the entire tax imposed. In this way, it appears to me, geometry originated, which passed thence to Hellas.
Heroditus
(II. c. 109) As quoted in Florian Cajori, A History of Elementary Mathematics (1893), 10, footnoted to C.A. Bretschneider, Die Geometrie und die Geometer vor Eukides (1870). Note that the word geometry itself means “land measurement.”
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Thus far I have explained the phenomena of the heavens and of our sea by the force of gravity, but I have not yet assigned a cause to gravity. Indeed, this force arises from some cause that penetrates as far as the centers of the sun and planets without any diminution of its power to act, and that acts not in proportion to the quantity of the surfaces of the particles on which it acts (as mechanical causes are wont to do) but in proportion to the quantity of solid matter, and whose action is extended everywhere to immense distances, always decreasing as the squares of the distances.
The Principia: Mathematical Principles of Natural Philosophy (1687), 3rd edition (1726), trans. I. Bernard Cohen and Anne Whitman (1999), General Scholium, 943.
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We all remember the fairy tales of science in our infancy, which played with the supposition that large animals could jump in the proportion of small ones. If an elephant were as strong as a grasshopper, he could (I suppose) spring clean out of the Zoological Gardens and alight trumpeting upon Primrose Hill. If a whale could leap from the water like a trout, perhaps men might look up and see one soaring above Yarmouth like the winged island of Laputa.
In Manalive (1912), 26.
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We have now felled forest enough everywhere, in many districts far too much. Let us restore this one element of material life to its normal proportions, and devise means for maintaining the permanence of its relations to the fields, the meadows and the pastures, to the rain and the dews of heaven, to the springs and rivulets with which it waters down the earth.
From Man and Nature (1864), 328-329.
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We’re going to see public attitudes [on climate change] switch not in proportion to scientific findings or graphs, but in proportion to the stories they hear, the people they know whose lives have been touched by climate change or some environmental calamity. That’s what really changed public opinion.
From interview with Mark Tercek, 'Q&A With Ramez Naam: Dialogues on the Environment', Huffington Post (1 Jul 2013).
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[Henry Cavendish] fixed the weight of the earth; he established the proportions of the constituents of the air; he occupied himself with the quantitative study of the laws of heat; and lastly, he demonstrated the nature of water and determined its volumetric composition. Earth, air, fire, and water—each and all came within the range of his observations.
Essays in Historical Chemistry (1894), 86.
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[To give insight to statistical information] it occurred to me, that making an appeal to the eye when proportion and magnitude are concerned, is the best and readiest method of conveying a distinct idea.
In The Statistical Breviary: Shewing, on a Principle Entirely New, the Resources of Every State and Kingdom in Europe (1801), 2.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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- 90 -
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- 70 -
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- 60 -
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